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To solve the resulting discrete nonlinear systems, a Newton method with exact Jacobian matrix is used.
The finite volume (FV) method with exact two-material Riemann problems (FIVER) is an Eulerian computational method for the solution of multi-material flow problems.
Governing equations are simplified to two partial differential equations using displacement potential functions (DPF) which are solved using the separation of variables method with exact satisfaction of boundary conditions.
The accuracy of the proposed scheme is assessed by comparison of the method with exact results obtained either by full finite element simulations in time-domain or by available analytical results obtained by the Laplace transform.
Our framework is based on the Fourier Galerkin method with exact and approximate integrations that has recently been shown to generalize the Lippmann Schwinger setting of the original work by Moulinec and Suquet from 1994.
Figure 2 Comparisons of exact solution and its approximations at (pmb{z=-10, 0, 2, 5}) with (pmb{varepsilon=0.05}) for Example 1. From Figures 1 and 2, and Table 3, we see that there is almost no difference for the a posteriori and a priori Fourier method with exact a priori bound E when r is relatively small.
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We compare the properties of these two methods with exact calculation according to objective criteria and present one example from a study conducted in France.
We compare the proposed methods with exact and heuristic algorithms for mixed integer non-linear programming problems, proving that our approach provides good-quality solutions in smaller CPU time.
Standard contingency table methods, with exact tests and when appropriate Mantel extension trend tests assessed univariate associations of categorical variables with CIN3 and cancer versus
Also, we compare the numerical solution obtained by using the proposed method with the exact solution.
Polak and Ribière [2] proved that the PRP method with the exact line search is globally convergent under a strong convexity assumption for the objective function f.
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